Best Known (13, ∞, s)-Nets in Base 81
(13, ∞, 224)-Net over F81 — Constructive and digital
Digital (13, m, 224)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
(13, ∞, 298)-Net over F81 — Digital
Digital (13, m, 298)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (13, 297)-sequence over F81, using
- t-expansion [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- t-expansion [i] based on digital (12, 297)-sequence over F81, using
(13, ∞, 1148)-Net in Base 81 — Upper bound on s
There is no (13, m, 1149)-net in base 81 for arbitrarily large m, because
- m-reduction [i] would yield (13, 1147, 1149)-net in base 81, but
- extracting embedded OOA [i] would yield OA(811147, 1149, S81, 1134), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 26 177184 104618 106859 864920 555527 638468 982709 409627 735767 914173 985950 578148 707171 220851 687693 625774 443832 757667 406184 960396 096881 462422 583125 319932 617289 032211 512422 963354 807301 390774 268696 909751 316505 691667 771350 285833 058357 430374 402224 681034 732882 920763 879678 407768 556929 466376 629268 235973 071018 252193 513320 597476 926038 606925 508518 987408 414037 758613 206309 807337 226383 944836 870824 206877 258284 106157 326643 834510 969749 329340 812938 509641 433666 204085 312458 277618 412481 183035 018215 575992 215000 848132 661089 768747 830865 869210 104800 999778 530731 298527 156246 125424 857726 520216 701452 836411 082519 588797 836995 771619 084959 120502 012808 892059 413743 683708 951476 957948 029022 297436 619554 257868 040121 075662 310868 636124 747943 464306 380984 124713 569460 994574 977955 104684 533795 191898 636938 304690 627981 049585 518592 049228 507709 629479 950223 705865 740872 088737 433067 895874 175895 949678 613923 016506 879607 336430 987479 777330 753067 057141 060682 804145 187506 224463 912758 885322 316221 678843 975940 173026 537139 446341 487095 362738 852645 007833 714502 507673 255939 000224 401178 587322 989155 698116 082794 632920 639780 197747 641080 586949 292228 688366 946431 448878 342701 676697 970959 553872 551553 981343 297829 401114 135627 943088 253105 948277 017053 907983 282450 761859 811849 158325 249334 307601 132330 572562 580793 367531 902714 247112 450342 397338 126009 360268 458661 486546 097155 867154 188332 153507 012184 653120 149408 687274 103803 669239 794256 683703 347070 631432 228503 260000 822554 376637 294570 375391 677501 656511 756482 978514 510216 912632 715964 516828 954504 715302 565488 858971 234208 944661 278327 038617 201655 666225 973901 290662 699537 992771 815308 568583 640514 983532 333854 995742 967842 713677 372100 868139 102268 672089 759023 424074 160407 844089 809066 717045 225545 751981 214968 742510 881602 549244 731581 242172 517398 053195 790447 456568 950599 597830 585158 231587 304657 331185 747918 371642 140111 845177 678081 683420 787248 303717 759756 890699 382020 224870 656979 413774 355091 760815 252550 037785 856593 611635 113446 741232 227440 016213 926339 157199 992959 885010 542780 122928 521357 360036 696201 653077 960301 107444 544305 748263 884363 477627 337020 779361 878804 106536 077187 882778 650018 677912 731155 820712 905686 382236 666645 946733 418490 348956 461905 348514 462834 823603 718809 980680 072839 484654 673038 418838 142226 218305 324423 610305 389123 / 227 > 811147 [i]
- extracting embedded OOA [i] would yield OA(811147, 1149, S81, 1134), but